It remains to discuss Verdier duality. Recall that if \(p\)  is invertible in the coefficient ring \(\mathbf {Z}/n\) , then [1]} shows that any separated taut morphism \(f: X \rightarrow Y\)  of rigid spaces over \(K\)  induces a well-behaved functor \(Rf_!: D(X,\mathbf {Z}/n) \rightarrow D(Y,\mathbf {Z}/n)\)  with a well-behaved right adjoint \(Rf^!\) . In particular, for any separated taut rigid space \(X\)  and any \(n\)  prime to \(p\) , we can define the dualizing complex \(\omega _X=R\pi _X^{!}(\mathbf {Z}/n)\) , where \(\pi _X : X \rightarrow \mathop {\mathrm {Spa}}\,K\)  is the structure map. We shall construct dualizing complexes in a different way using results from [2]}; our construction works without restriction on \(p\) , and is equivalent to Huber's if \((p,n)=1\) . We will need the following form of unbounded BBDG gluing [3]} for complexes.
